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Two basic boundary-value problems for the inhomogeneous Cauchy–Riemann equation in an infinite sector
-
Mohamed S. Akel
and
Hussein S. Hussein
Published/Copyright:
August 1, 2012
Abstract.
The object of the present article is to investigate the Schwarz and
Dirichlet boundary value problems for the inhomogeneous Cauchy–Riemann equation in an infinite sector. Firstly, we obtain the Schwarz–Poisson formula in a sector with angle 
(
). Secondly, boundary behaviors of some linear integrals will be studied, especially at the corner point. Finally, the solutions and the conditions of solvability are explicitly obtained.
Keywords: Cauchy–Pompeiu formula; inhomogeneous Cauchy–Riemann equation; Schwarz-type operator; Pompeiu-type operator; Schwarz problem; Dirichlet problem
Received: 2011-09-15
Revised: 2012-06-03
Accepted: 2012-06-03
Published Online: 2012-08-01
Published in Print: 2012-08-01
© 2012 by Walter de Gruyter Berlin Boston
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Keywords for this article
Cauchy–Pompeiu formula;
inhomogeneous Cauchy–Riemann equation;
Schwarz-type operator;
Pompeiu-type operator;
Schwarz problem;
Dirichlet problem
Articles in the same Issue
- Masthead
- Analytic properties of the Hasse–Weil L-function
- A note on absolute Cesàro summability factors
- Analogues to some uncertainty principles on certain solvable Lie groups
- The interplay between the CR “flatness condition” and existence results for the prescribed Webster scalar curvature
- On generalized Gajda's functional equation of D'Alembert type
- Two basic boundary-value problems for the inhomogeneous Cauchy–Riemann equation in an infinite sector
- Joint dilation scaling sets on the reducing subspaces
